Low-rank modeling generally refers to a class of methods that solves
problems by representing variables of interest as low-rank matrices. It
has achieved great success in various fields including computer vision,
data mining, signal processing, and bioinformatics. Recently, much
progress has been made in theories, algorithms, and applications of
low-rank modeling, such as exact low-rank matrix recovery via convex
programming and matrix completion applied to collaborative filtering.
These advances have brought more and more attention to this topic. In
this article, we review the recent advances of low-rank modeling, the
state-of-the-art algorithms, and the related applications in image
analysis. We first give an overview of the concept of low-rank modeling
and the challenging problems in this area. Then, we summarize the models
and algorithms for low-rank matrix recovery and illustrate their
advantages and limitations with numerical experiments. Next, we
introduce a few applications of low-rank modeling in the context of
image analysis. Finally, we conclude this article with some discussions.

From the paper:

In this paper, we have introduced the concept of low-rank modeling and reviewed some representative low-rank models, algorithms and applications in image analysis. For additional reading on theories, algorithms and applications, the readers are referred to online documents such as the Matrix Factorization Jungle3 and the Sparse and Low-rank Approximation Wiki4, which are updated on a regular basis.